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Inversion is geophysical inversion software for magnetic and gravity profile data. It is using Werner deconvolution to compute approximate position of singularities of anomalous bodies. For detailed description see Werner deconvolution. 
\par 
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Werner (1953), analysing the magnetic field of arbitrary dikes, proposed a method for it\rquote 
s interpretation. This method deals with 2-D problems. By solving the systems of linear equations we can find, either, under assumption of a thin dike object from }{\lang2057\langfe1033\langnp2057 {\field{\*\fldinst SYMBOL 68 \\f "Symbol" \\s 12}{\fldrslt
\f3\fs24}}}{\lang2057\langfe1033\langnp2057 T curve it\rquote s upper edge, or under assumption of a thick dike, from }{\lang2057\langfe1033\langnp2057 {\field{\*\fldinst SYMBOL 182 \\f "Symbol" \\s 12}{\fldrslt\f3\fs24}}}{\lang2057\langfe1033\langnp2057 
(}{\lang2057\langfe1033\langnp2057 {\field{\*\fldinst SYMBOL 68 \\f "Symbol" \\s 12}{\fldrslt\f3\fs24}}}{\lang2057\langfe1033\langnp2057 T)/}{\lang2057\langfe1033\langnp2057 {\field{\*\fldinst SYMBOL 182 \\f "Symbol" \\s 12}{\fldrslt\f3\fs24}}}{
\lang2057\langfe1033\langnp2057 x curve its upper edges. Although the simplification seems to be a limitation, the method does provide a wide range of applications. Advantages and limitations of the process of inversion will be discussed in this chapter.

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{\*\bkmkend _Toc480367066}{\*\bkmkend _Toc480643092}{\*\bkmkend _Toc480678940}
\par {\*\bkmkstart _Toc480106848}{\*\bkmkstart _Toc480107496}{\*\bkmkstart _Toc480107725}{\*\bkmkstart _Toc480107945}{\*\bkmkstart _Toc480108082}{\*\bkmkstart _Toc480108309}{\*\bkmkstart _Toc480108400}{\*\bkmkstart _Toc480108500}{\*\bkmkstart _Toc480108649}
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\b\fs24\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\lang2057\langfe1033\langnp2057 Thin dike {\*\bkmkend _Toc480106848}{\*\bkmkend _Toc480107496}{\*\bkmkend _Toc480107725}{\*\bkmkend _Toc480107945}{\*\bkmkend _Toc480108082}
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Assuming the well-known formulae for magnetic scalar potential (1.1) we can derive an equation for arbitrary 2-D body (e.g. Talwani & Heirtzer, 1964; Ku & Sharp, 1983). We choose the }{\i\lang2057\langfe1033\langnp2057 x}{\lang2057\langfe1033\langnp2057 -
axis perpendicular to the strike of the dike, the }{\i\lang2057\langfe1033\langnp2057 y}{\lang2057\langfe1033\langnp2057 -axis parallel to the strike, and the }{\i\lang2057\langfe1033\langnp2057 z}{\lang2057\langfe1033\langnp2057 
-axis vertical. Equations for vertical, horizontal and total magnetic anomalies are
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\i\lang2057\langfe1033\langnp2057 M}{\i\lang2057\langfe1033\sub\langnp2057 x}{\lang2057\langfe1033\langnp2057 , }{\i\lang2057\langfe1033\langnp2057 M}{\i\lang2057\langfe1033\sub\langnp2057 z}{\lang2057\langfe1033\langnp2057 ) is the magnetisation vector }
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\par }\pard \s15\qj \li0\ri0\widctlpar{\*\pn \pnlvlcont\ilvl0\ls0\pnrnot0\pndec }\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\lang2057\langfe1033\langnp2057 where
\par 
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\lang2057\langfe1033\langnp2057 ,\tab \tab \tab \tab \tab (1.8)
\par }\pard \s15\qj \li0\ri0\widctlpar{\*\pn \pnlvlcont\ilvl0\ls0\pnrnot0\pndec }\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\i\lang2057\langfe1033\langnp2057 
\par I}{\lang2057\langfe1033\langnp2057 \~is a magnetic inclination of the main field }{\b\lang2057\langfe1033\langnp2057 T}{\lang2057\langfe1033\langnp2057 ; }{\lang2057\langfe1033\langnp2057 {\field{\*\fldinst SYMBOL 97 \\f "Symbol" \\s 12}{\fldrslt
\f3\fs24}}}{\lang2057\langfe1033\langnp2057  is a strike of the dike measured from the magnetic north, positive clockwise.}{\i\lang2057\langfe1033\langnp2057 
\par }{\lang2057\langfe1033\langnp2057 For an arbitrary location of the dike (}{\i\lang2057\langfe1033\langnp2057 x}{\i\lang2057\langfe1033\sub\langnp2057 0}{\lang2057\langfe1033\langnp2057 ,}{\i\lang2057\langfe1033\langnp2057  h}{
\i\lang2057\langfe1033\sub\langnp2057 0}{\lang2057\langfe1033\langnp2057 ) on a profile (}{\i\lang2057\langfe1033\langnp2057 x}{\lang2057\langfe1033\langnp2057 , 0), equation (4.5) becomes
\par 
\par }\pard \s15\qr \li0\ri0\widctlpar{\*\pn \pnlvlcont\ilvl0\ls0\pnrnot0\pndec }\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\pard\plain \s15\qr \li0\ri0\widctlpar{\*\pn \pnlvlcont\ilvl0\ls0\pnrnot0\pndec }
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\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw4621\pich1235\picwgoal2620\pichgoal700\wmetafile8\bliptag-1309022607\blipupi266{\*\blipuid b1f9e6710c17f8250d7e51d61fbd70ab}
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\tab \tab \tab \tab          (1.9)
\par }\pard \s15\qc \li0\ri0\widctlpar{\*\pn \pnlvlcont\ilvl0\ls0\pnrnot0\pndec }\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\lang2057\langfe1033\langnp2057 
\par }\pard \s15\qj \li0\ri0\widctlpar{\*\pn \pnlvlcont\ilvl0\ls0\pnrnot0\pndec }\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\lang2057\langfe1033\langnp2057 or
\par 
\par }\pard \s15\qr \li0\ri0\widctlpar{\*\pn \pnlvlcont\ilvl0\ls0\pnrnot0\pndec }\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\pard\plain \s15\qr \li0\ri0\widctlpar{\*\pn \pnlvlcont\ilvl0\ls0\pnrnot0\pndec }
\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\object\objemb\objw3081\objh380{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e33000000000000000000000c0000
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\par }\pard \s15\qc \li0\ri0\widctlpar{\*\pn \pnlvlcont\ilvl0\ls0\pnrnot0\pndec }\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\lang2057\langfe1033\langnp2057 
\par }\pard \s15\qj \li0\ri0\widctlpar{\*\pn \pnlvlcont\ilvl0\ls0\pnrnot0\pndec }\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\lang2057\langfe1033\langnp2057 
This equation is referred to be a Werner four-point operator, and its properties will be discussed in chapter 4.1.3.
\par {\*\bkmkstart _Toc480106849}{\*\bkmkstart _Toc480107497}{\*\bkmkstart _Toc480107726}{\*\bkmkstart _Toc480107946}{\*\bkmkstart _Toc480108083}{\*\bkmkstart _Toc480108310}{\*\bkmkstart _Toc480108401}{\*\bkmkstart _Toc480108501}{\*\bkmkstart _Toc480108650}
{\*\bkmkstart _Toc480366886}{\*\bkmkstart _Toc480366949}{\*\bkmkstart _Toc480367068}{\*\bkmkstart _Toc480643094}{\*\bkmkstart _Toc480678942}{\pntext\pard\plain\s3 \b\lang2057\langfe1033\langnp2057 \hich\af0\dbch\af0\loch\f0 2.\tab}}\pard\plain 
\s3\ql \li1701\ri0\sb240\sa60\keepn\widctlpar{\*\pn \pnlvlbody\ilvl2\ls3\pnrnot0\pndec\pnstart1\pnindent360\pnhang{\pntxtb .}}\aspalpha\aspnum\faauto\ls3\ilvl2\outlinelevel2\adjustright\rin0\lin1701\itap0 
\b\fs24\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\lang2057\langfe1033\langnp2057 Generalisation of Werner deconvolution{\*\bkmkend _Toc480106849}{\*\bkmkend _Toc480107497}{\*\bkmkend _Toc480107726}{\*\bkmkend _Toc480107946}
{\*\bkmkend _Toc480108083}{\*\bkmkend _Toc480108310}{\*\bkmkend _Toc480108401}{\*\bkmkend _Toc480108501}{\*\bkmkend _Toc480108650}{\*\bkmkend _Toc480366886}{\*\bkmkend _Toc480366949}{\*\bkmkend _Toc480367068}{\*\bkmkend _Toc480643094}
{\*\bkmkend _Toc480678942}
\par }\pard\plain \s15\qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \fs24\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\lang2057\langfe1033\langnp2057 
\par }\pard \s15\qj \fi360\li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\lang2057\langfe1033\langnp2057 
In this chapter brief generalisation of the Werner deconvolution is given. Only equations are to be written. For further reading see original papers.
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\aspalpha\aspnum\faauto\ls39\adjustright\rin0\lin360\itap0 {\lang2057\langfe1033\langnp2057 Magnetic
\par }\pard \s15\qj \li360\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin360\itap0 {\lang2057\langfe1033\langnp2057 Thin dike (Werner, 1953)
\par 
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\par }\pard \s15\qj \li360\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin360\itap0 {\lang2057\langfe1033\langnp2057 
\par For a\~thick dike edge we can write (Ku & Sharp, 1983):
\par 
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\par {\pntext\pard\plain\s15 \f3\lang2057\langfe1033\langnp2057 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \s15\qj \fi-360\li360\ri0\widctlpar\jclisttab\tx360{\*\pn \pnlvlblt\ilvl0\ls40\pnrnot0\pnf3\pnstart1\pnindent360\pnsp120\pnhang{\pntxtb \'b7}}
\aspalpha\aspnum\faauto\ls40\adjustright\rin0\lin360\itap0 {\lang2057\langfe1033\langnp2057 Gravity
\par }\pard \s15\qj \li360\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin360\itap0 {\lang2057\langfe1033\langnp2057 2-D cylinder (Dobrin, 1976, in Kilty, 1983):
\par 
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\par 
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\par 
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\lang2057\langfe1033\langnp2057 .
\par }\pard \s15\qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\lang2057\langfe1033\langnp2057 
\par The goal is that all above equations can be rewritten in the form of equation (4.10) and they can be solved similarly as in classical Werner deconvolution for unknown parameters }{\i\lang2057\langfe1033\langnp2057 x}{\i\lang2057\langfe1033\sub\langnp2057 
0}{\lang2057\langfe1033\langnp2057 , }{\i\lang2057\langfe1033\langnp2057 z}{\i\lang2057\langfe1033\sub\langnp2057 0}{\lang2057\langfe1033\langnp2057 .
\par {\*\bkmkstart _Toc314490348}{\*\bkmkstart _Toc314490461}{\*\bkmkstart _Toc480106850}{\*\bkmkstart _Toc480107498}{\*\bkmkstart _Toc480107727}{\*\bkmkstart _Toc480107947}{\*\bkmkstart _Toc480108084}{\*\bkmkstart _Toc480108311}{\*\bkmkstart _Toc480108402}
{\*\bkmkstart _Toc480108502}{\*\bkmkstart _Toc480108651}{\*\bkmkstart _Toc480366887}{\*\bkmkstart _Toc480366950}{\*\bkmkstart _Toc480367069}{\*\bkmkstart _Toc480643095}{\*\bkmkstart _Toc480678943}{\pntext\pard\plain\s3 \b\lang2057\langfe1033\langnp2057 
\hich\af0\dbch\af0\loch\f0 3.\tab}}\pard\plain \s3\ql \li1701\ri0\sb240\sa60\keepn\widctlpar{\*\pn \pnlvlbody\ilvl2\ls3\pnrnot0\pndec\pnstart1\pnindent360\pnhang{\pntxtb .}}\aspalpha\aspnum\faauto\ls3\ilvl2\outlinelevel2\adjustright\rin0\lin1701\itap0 
\b\fs24\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\lang2057\langfe1033\langnp2057 Properties of the Werner n-point operator{\*\bkmkend _Toc314490348}{\*\bkmkend _Toc314490461}{\*\bkmkend _Toc480106850}{\*\bkmkend _Toc480107498}
{\*\bkmkend _Toc480107727}{\*\bkmkend _Toc480107947}{\*\bkmkend _Toc480108084}{\*\bkmkend _Toc480108311}{\*\bkmkend _Toc480108402}{\*\bkmkend _Toc480108502}{\*\bkmkend _Toc480108651}{\*\bkmkend _Toc480366887}{\*\bkmkend _Toc480366950}
{\*\bkmkend _Toc480367069}{\*\bkmkend _Toc480643095}{\*\bkmkend _Toc480678943}
\par }\pard\plain \ql \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \fs24\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\lang2057\langfe1033\langnp2057 
\par }\pard\plain \s15\qj \fi720\li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \fs24\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\lang2057\langfe1033\langnp2057 In this chapter we are going to discuss the properties of the Werner 
}{\i\lang2057\langfe1033\langnp2057 n}{\lang2057\langfe1033\langnp2057 -point operator from the point of view of theory, where }{\i\lang2057\langfe1033\langnp2057 n}{\lang2057\langfe1033\langnp2057 -point operator means that we are solving }{
\i\lang2057\langfe1033\langnp2057 n}{\lang2057\langfe1033\langnp2057  equations of either }{\i\lang2057\langfe1033\langnp2057 n}{\lang2057\langfe1033\langnp2057  or more unknowns. 
\par Let us rewrite the interpretation equation (4.9) in the form
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\par }\pard \s15\qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\lang2057\langfe1033\langnp2057 
\par or in the form
\par 
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\par }\pard \s15\qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\lang2057\langfe1033\langnp2057 
\par I prefer to write the interpretation equation in the form written above, because of clarity of the following discussion.
\par }\pard \s15\qj \fi720\li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\lang2057\langfe1033\langnp2057 Now let us assume Werner\rquote s interference polynomial in the form
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\par }\pard \s15\qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\outlinelevel0\adjustright\rin0\lin0\itap0 {\lang2057\langfe1033\langnp2057 From the equations (4.15) we have 
\par }\pard \s15\qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\lang2057\langfe1033\langnp2057 
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\par }\pard \s15\qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\lang2057\langfe1033\langnp2057 
\par where }{\b\lang2057\langfe1033\langnp2057 d}{\lang2057\langfe1033\langnp2057 , }{\b\lang2057\langfe1033\langnp2057 d}{\lang2057\langfe1033\langnp2057  = (}{\i\lang2057\langfe1033\langnp2057 d}{\lang2057\langfe1033\sub\langnp2057 0}{
\lang2057\langfe1033\langnp2057  }{\i\lang2057\langfe1033\langnp2057 d}{\lang2057\langfe1033\sub\langnp2057 1}{\lang2057\langfe1033\langnp2057  }{\i\lang2057\langfe1033\langnp2057 d}{\lang2057\langfe1033\sub\langnp2057 2}{\lang2057\langfe1033\langnp2057 
 . . . }{\i\lang2057\langfe1033\langnp2057 d}{\lang2057\langfe1033\sub\langnp2057 n}{\lang2057\langfe1033\langnp2057 ) is \'93solution\'94 vector, }{\i\lang2057\langfe1033\langnp2057 n}{\lang2057\langfe1033\langnp2057 
+1 is the number of terms on the right-hand side of the equation (4.14). The equation (4.16) gives solution for depth and location of the dike; from parameters }{\i\lang2057\langfe1033\langnp2057 A}{\lang2057\langfe1033\langnp2057  and }{
\i\lang2057\langfe1033\langnp2057 B}{\lang2057\langfe1033\langnp2057  we can compute dip and susceptibility, and parameters of the interference polynomial }{\i\lang2057\langfe1033\langnp2057 c}{\lang2057\langfe1033\sub\langnp2057 0}{
\lang2057\langfe1033\langnp2057 ,\~}{\i\lang2057\langfe1033\langnp2057 c}{\lang2057\langfe1033\sub\langnp2057 1}{\lang2057\langfe1033\langnp2057 ,\~}{\i\lang2057\langfe1033\langnp2057 c}{\lang2057\langfe1033\sub\langnp2057 2}{
\lang2057\langfe1033\langnp2057 ,\~}{\lang2057\langfe1033\langnp2057 {\field{\*\fldinst SYMBOL 188 \\f "Symbol" \\s 12}{\fldrslt\f3\fs24}}}{\lang2057\langfe1033\langnp2057 ,\~}{\i\lang2057\langfe1033\langnp2057 c}{\lang2057\langfe1033\sub\langnp2057 n-2}{
\lang2057\langfe1033\langnp2057 .
\par 
\par As long as we have computed parameters }{\i\lang2057\langfe1033\langnp2057 A}{\lang2057\langfe1033\langnp2057 , }{\i\lang2057\langfe1033\langnp2057 B}{\lang2057\langfe1033\langnp2057 
 we can derive susceptibility contrast and the dip of the dike. Recalling the equations (4.7) we have
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\tab (1.18)
\par }\pard \s15\qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\lang2057\langfe1033\langnp2057 
\par where }{\i\lang2057\langfe1033\langnp2057 I}{\lang2057\langfe1033\langnp2057 \~is magnetic inclination.
\par 
\par }\pard \s15\qj \fi709\li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\lang2057\langfe1033\langnp2057 
Now look closer at the equations, and try to examine, how computed parameters affect a solution. The right-hand side of the equation (4.15) co
ntains all pieces of information about the magnetic inclination, declination, strike, dip and susceptibility of the dike (parameters }{\i\lang2057\langfe1033\langnp2057 a}{\i\lang2057\langfe1033\sub\langnp2057 i}{\lang2057\langfe1033\langnp2057 
). We can see, that changes in the parameters }{\i\lang2057\langfe1033\langnp2057 a}{\i\lang2057\langfe1033\sub\langnp2057 i}{\lang2057\langfe1033\langnp2057  of a dike, related with the right-hand side of the equation (4.15), do }{
\b\lang2057\langfe1033\langnp2057 not}{\lang2057\langfe1033\langnp2057  in fact affect a solution for depth and position of a dike. It happens rarely, that we can find the exact position of a\~
geological body, although we do not know any other parameters of a body. On the other hand, parameters }{\i\lang2057\langfe1033\langnp2057 b}{\i\lang2057\langfe1033\sub\langnp2057 i}{\lang2057\langfe1033\langnp2057  affects the solution of the
 inclination, strike }{\lang2057\langfe1033\langnp2057 {\field{\*\fldinst SYMBOL 188 \\f "Symbol" \\s 12}{\fldrslt\f3\fs24}}}{\lang2057\langfe1033\langnp2057  see equations (4.16). 
\par {\pntext\pard\plain\s15 \f3\lang2057\langfe1033\langnp2057 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \s15\qj \fi-360\li360\ri0\widctlpar\jclisttab\tx360{\*\pn \pnlvlblt\ilvl0\ls24\pnrnot0\pnf3\pnstart1\pnindent360\pnsp120\pnhang{\pntxtb \'b7}}
\aspalpha\aspnum\faauto\ls24\adjustright\rin0\lin360\itap0 {\lang2057\langfe1033\langnp2057 The remnant magnetisation does not affect the solution for depth and position of the dike. 
\par }\pard \s15\qj \li360\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin360\itap0 {\b\lang2057\langfe1033\langnp2057 Proof}{\lang2057\langfe1033\langnp2057 : Due to the superposition principle we can write
\par 
\par }\pard \s15\qr \li360\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin360\itap0 {\pard\plain \s15\qr \li360\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin360\itap0 \fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\object\objemb
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\par }\pard \s15\qc \li360\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin360\itap0 {\lang2057\langfe1033\langnp2057 
\par }\pard \s15\qj \li360\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin360\itap0 {\lang2057\langfe1033\langnp2057 where coefficients A}{\lang2057\langfe1033\sub\langnp2057 R}{\lang2057\langfe1033\langnp2057  and B}{
\lang2057\langfe1033\sub\langnp2057 R}{\lang2057\langfe1033\langnp2057  are for the remnant magnetisation.
\par  Then
\par 
\par }\pard \s15\qr \li360\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin360\itap0 {\pard\plain \s15\qr \li360\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin360\itap0 \fs24\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\object\objemb
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\par }\pard \s15\qc \li360\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin360\itap0 {\lang2057\langfe1033\langnp2057 
\par }\pard \s15\qj \li360\ri0\widctlpar\aspalpha\aspnum\faauto\outlinelevel0\adjustright\rin0\lin360\itap0 {\lang2057\langfe1033\langnp2057 The equation (4.22) equals to (4.12). q.e.d.
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\par }\pard \s15\qj \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\lang2057\langfe1033\langnp2057 If the induced magnetisation is known (what is true), we can compute remnant magnetisation.
\par }\pard \s15\qj \fi567\li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\lang2057\langfe1033\langnp2057 
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f001000008000000320aa001ee0301000000410009000000320aa001340004000000636f6e640a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000ee0102022253797374656d00ee040000002d01000004000000f0010100030000000000}}}}}{
\lang2057\langfe1033\langnp2057 ). Such a systems of linear equations do not have solutions in a sense of classical numerical analysis. One possible way is to use regularisation. 
\par }\pard \s15\qj \fi360\li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 {\lang2057\langfe1033\langnp2057 Sensitiv
ity to the noise: Recall the equation (3.48) of the condition number and the chapter about SVD. From discussion about SVD we can see that small error either in measured data }{\b\lang2057\langfe1033\langnp2057 b}{\lang2057\langfe1033\langnp2057 
 or coefficients of the matrix }{\b\lang2057\langfe1033\langnp2057 A}{\lang2057\langfe1033\langnp2057 \~can cause unacceptable error in the solution. The condition numbers of the systems of linear equations solved in Werner deconvolution are ~10}{
\lang2057\langfe1033\super\langnp2057 4}{\lang2057\langfe1033\langnp2057 \~\endash \~10}{\lang2057\langfe1033\super\langnp2057 30}{\lang2057\langfe1033\langnp2057 
 (ideal is 1), what means that the systems are ill conditioned. For this reason small perturbations may cause that the solution fails. 
\par }\pard\plain \ql \li0\ri0\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0 \fs24\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\lang2057\langfe1033\langnp2057 
\par }{
\par }}